Evaluate f(x)=4|x|+3 for x=-5

Mathematics

1 answer:

ratelena [41]2 years ago

4 0

Subs x = -5 into f(x) = 4

f(-5) = 4 (answer)

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James used substitution to solve this system of equations which equation could be the result of his first step?

vaieri [72.5K]

Answer: OPTION D.

Step-by-step explanation:

<h3> The compete exercise is: "James used substitution to solve this system of equations. Which could be the result of his first step</h3><h3> $\left \{ {{2x+3y=12} \atop {y=x+1.5}} \right.\\\\\\A.y=2x+3y\\B.y=2x+3y+1.5\\C.2x+3x+1.5=12\\D.2x+3(x+1.5)=12$ "</h3>

Given the sytsem of equations:

$\left \{ {{2x+3y=12} \atop {y=x+1.5}} \right.$

1- Solve for one of the variables from any equation and substitute it into the other equation.

2- Solve for the other variable in order to get its value.

3- Substitute this value back into one of the original equations. and find the value of the other variable.

In this case youu can observe that the second equation is already solved for "y", therefore, in order to use the Substitution Method, the first step is: Substitute the second equation into the first one.

Therefore, the equation that could be the result of James' first step is:

$2x+3y=12\\\\2x+3(x+1.5)=12$

5 0

4 years ago

Read 2 more answers

A small garden measures 9 ft by 13 ft. A uniform border around the garden increases the total area to 192 ft square. What is the

victus00 [196]

The width of border is 1.5 feet

<h3><u>Solution:</u></h3>

Given that small garden measures 9 ft by 13 ft

A uniform border around the garden increases the total area to 192 ft square

To find: width of border

Let the width of border be "x"

Then the new measures of garden are (9 + 2x) feet and (13 + 2x) feet

The total area of garden = 192 square feet

$(9 + 2x)(13 + 2x) =192$

$117 + 18x + 26x + 4x^2 = 192\\\\4x^2 + 44x - 75 = 0$

<em><u>Let us solve the above equation by quadratic formula</u></em>

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

For $4x^2 + 44x - 75 = 0$ , we have a = 4 ; b = 44 ; c = -75

Substituting the values of a = 4 ; b = 44 ; c = -75 in above quadratic formula we get,

$\begin{aligned}&x=\frac{-44 \pm \sqrt{44^{2}-4(4)(-75)}}{2 \times 4}\\\\&x=\frac{-44 \pm \sqrt{1936-1200}}{8}\\\\&x=\frac{-44 \pm \sqrt{3136}}{8}\\\\&x=\frac{-44 \pm 56}{8}\end{aligned}$

$\begin{aligned}&x=\frac{-44+56}{8} \text { or } x=\frac{-44-56}{8}\\\\&x=\frac{12}{8} \text { or } x=\frac{-100}{8}\\\\&x=1.5 \text { or } x=-12.5\end{aligned}$